Sequencing Animations in Animation Nodes
Animation Nodes already provide such nesting functionality in the Animate nodes, and you can similarly implement an equivalent functionality if you choose not to use the native Animate nodes.

An Animate node interpolates between two values for a certain duration. For instance, if the start value was 0, the end value was 5, and the duration was 20, then the output will gradually increase from 0 based on the chosen interpolation for 20 frames where it reaches 5 at the 20th frame.

But what about the frame at which the animation starts, how do we define that? Well, Animation Nodes always starts the animation at frame zero. However, the frame/time is exposed as an input in the Animate node, so what we can do is edit this input frame/time such that it becomes zero at the frame we want the animation to start at. This is easily done by subtracting the target starting frame $f_t$ from the scene or master frame $f_m$, because when the master frame becomes equal to the target frame our equation returns zero  $f_m-f_t = 0$. This is what the Delay node does, it simply subtracts the input, nothing more, nothing less.

Now, the Animate node provides a Time output. This output is the input time minus the duration. Think about that for a second. It means that if the output time of an Animate node $A$ is used as the input time of another Animate node $B$, the $B$ animation will start as soon as the $A$ animation ends. Now, if I delay (by subtracting) the output time of the node $A$ by 5 frames and use it as the input time of the node $B$, then the $B$ animation will start after the $A$ animation ends by 5 frames. And so on.

So, to implement a sequence of animations, use a chain of Animate nodes where the input time of each node is the output time of the previous with a possible delay (With the first node having the master time as its input, also with a possible delay). Want to add an animation at the start of the sequence, no problem, just put this node first. So the node tree should look like this: